Answer
Point-slope form:
$y=-5(x+2)$
Function notation of the slope-intercept form:
$f(x) =-5x-10$
Work Step by Step
RECALL:
(i) The point-slope form of a line's equation is:
$y-y_1=m(x-x_1)$
where
m= slope and $(x_1, y_1)$ is a point on the line.
(ii) The function notation of the slope-intercept form of a line's equation is:
$f(x) = mx + b$
where
m= slope and b = y-intercept
The given line has $m=-5$ and passes through the point (-2, 0). This means that the point-slope form of the line's equation is:
$y-0 = -5[x-(-2)]
\\y=-5(x+2)$
Convert the equation to slope-intercept form by distributing $-5$ to obtain:
$y =-5(x+2)
\\y=-5\cdot x + (-5)\cdot 2
\\y=-5x+(-10)
\\y=-5x-10$
In function notation, the slope-intercept form of the equation is:
$f(x) = -5x-10$
